Fermionic functionals without Grassmann numbers

TL;DR

This paper introduces a Grassmann-free functional formalism for fermionic operators, enabling faster numerical lattice computations by using eigenvalues of hermitian components, simplifying fermionic calculations.

Contribution

The authors develop a novel fermionic functional formalism based on eigenvalues of hermitian operators, avoiding Grassmann numbers and improving computational efficiency.

Findings

Allows numerical fermionic lattice computations without Grassmann variables

Achieves faster calculations compared to existing fermionic algorithms

Simplifies fermionic operator matrix element evaluations

Abstract

Since any fermionic operator \psi can be written as \psi=q+ip, where q and p are hermitian operators, we use the eigenvalues of q and p to construct a functional formalism for calculating matrix elements that involve fermionic fields. The formalism is similar to that for bosonic fields and does not involve Grassmann numbers. This makes possible to perform numerical fermionic lattice computations that are much faster than not only other algorithms for fermions, but also algorithms for bosons.